We study the bilayer two-orbital model for superconducting pairing symmetry
of La3βNi2βO7β under pressure. By combining density-functional-theory
(DFT), maximally-localized-Wannier-function, and linearized Eliashberg equation
with random-phase-approximation, we find that the superconducting pairing
symmetry of La3βNi2βO7β is robustly dxyβ if its DFT band structure is
accurately reproduced in the downfolded model. We further show that fine-tuning
of crystal-field-splitting between two Ni-egβ orbitals qualitatively affects
superconducting pairing symmetry of the bilayer two-orbital model, which
changes from dxyβ to sΒ±β as the crystal-field-splitting exceeds a
critical value. When the model only includes nearest-neighbor and
second-nearest-neighbor hoppings, the crystal-field-splitting obtained by
fitting to the DFT band structure is larger than the critical value and thus
leads to sΒ±β superconducting pairing symmetry. When all nonzero
long-range-hoppings are also included in the model, the fitted
crystal-field-splitting is reduced and smaller than the critical value, which
makes dxyβ superconducting pairing symmetry more favorable than sΒ±β
symmetry. Our work demonstrates that in downfolded effective models, the
details of band structure can play a crucial role in determining pairing
symmetry in multi-orbital unconventional superconductors (such as
La3βNi2βO7β).Comment: 11 pages and 4 figure